Answer:
The shorter leg is five feet, the longer leg is 12 feet, and the hypotenuse is 13 feet.
Step-by-step explanation:
Let the shorter leg be <em>x</em>.
Since the longer leg is seven feet longer than the shorter leg, the length of the longer leg can be modeled by (<em>x</em> + 7).
Since the triangle is a right triangle, we can use the Pythagorean Theorem, given by:

Where <em>a</em> and <em>b</em> are the side lengths and <em>c</em> is the hypotenuse.
The hypotenuse is 13 and the legs are <em>x</em> and (<em>x</em> + 7). Substitute:

Square:

Simplify:

We can divide both sides by two:

Factor:

Zero Product Property:

Solve for each case:

Since lengths cannot be negative, we can ignore the negative answer. So, our only solution is:

The shorter leg is five feet, the longer leg will be (5 + 7) or 12 feet. And the hypotenuse is 13 feet as given.